QuestionAugust 25, 2025

Example 2: Write the domain and range of the function in both inequality notation and interval notation. sqrt [3](2x-7)

Example 2: Write the domain and range of the function in both inequality notation and interval notation. sqrt [3](2x-7)
Example 2: Write the domain and range of the function in both inequality notation and interval notation. sqrt [3](2x-7)

Solution
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Answer

Domain: (-\infty, \infty); Range: (-\infty, \infty) Explanation 1. Determine the Domain The function f(x) = \sqrt[3]{2x-7} is defined for all real numbers because cube roots are defined for all real inputs. Thus, the domain in inequality notation is -\infty < x < \infty and in interval notation is (-\infty, \infty). 2. Determine the Range Since cube root functions can produce any real number output, the range is also all real numbers. Therefore, the range in inequality notation is -\infty < y < \infty and in interval notation is (-\infty, \infty).

Explanation

1. Determine the Domain<br /> The function $f(x) = \sqrt[3]{2x-7}$ is defined for all real numbers because cube roots are defined for all real inputs. Thus, the domain in inequality notation is $-\infty < x < \infty$ and in interval notation is $(-\infty, \infty)$.<br /><br />2. Determine the Range<br /> Since cube root functions can produce any real number output, the range is also all real numbers. Therefore, the range in inequality notation is $-\infty < y < \infty$ and in interval notation is $(-\infty, \infty)$.
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